Tagged Questions

Questions about Turing computability and recursion theory, including the halting problem and other unsolvable problems. Questions about the resources required to solving particular problems should be tagged (computational-complexity).

The example is "left to the reader", but I am having trouble approaching this problem.
There is a primitive recursive function $tr$ such that if $s$ codes a sequence $(a_{0},...,a_{n-1})$, and $m\le ...

I've been having a lot of difficulty even beginning this problem. I believe that I would have to use the min and max functions, but I'm not entirely sure how to actually write this down rigorously, or ...

I would like to understand the rationale behind the oracle machine notation with brackets $\{e\}^A$ which is equivalent to $\phi_e^A$ where $A$ denotes the oracle set and $e$ denotes the index of the ...

Given any function $f: \mathbb{N}_0 \rightarrow \mathbb{N}_0$ and a recursive $h:\mathbb{N}_0 \rightarrow \mathbb{N}_0$ , I know that to prove $h\circ f$ is recursive I only need to prove that $f$ is ...

In studying properties of polynomial functions I have read that they are computable. The usage of the word read implies that I cannot prove this statement, and withhold using learned for this reason. ...

In "On formally undecidable propositions..." he writes a function is recursive if "... it is a constant or the successor function" is he referring to the constant function c(x)=k, and if so, is this ...

I am attempting to recreate an Excel Spreadsheet Dynamic Model (Figure 9.4) presented in my Data Warehousing Decision Support System course. I've uploaded a copy at the following link: Excel Link - On ...

The Chaitin constant can in principle be computed with exponential effort on each sucessive digit by brute forcing all programs of a given length and simply proving special theorems on each case that ...

What is the formal language described by inverting accepting states of NFA? By inverting, I mean that rejecting states become accepting states and accepting states become rejecting states.
Is there a ...

Several authors (e.g. Jockusch, Appel, McLaughlin) use a notion of a regressive set, however none of the authors gives a complete definition, they refer to the paper J. C. E. Dekker, Infinite series ...

I've been doing some work with factorials and the normal way of calculating them is simply not working so well. When the numbers get really big, doing iterative multiplications is not viable and gets ...

I have seen a definition (e.g. http://www.math.ubc.ca/~bwallace/ArithmeticalHierarchy.pdf) of an arithmetical hierarchy in computability starting with: "let $\Delta_0=\Sigma_0=\Pi_0$ be the set of all ...

I need to prove that, given a computable binary tree $T$ whose paths are exactly the complete extensions of $PA$ (via some Gödel coding), there is a computable $X\subseteq\mathbb{N}$ such that for all ...

As title says, if a set $\Sigma$ of alphabets is of cardinality $k$, does $\Sigma^n$ have cardinality of $k^n$? This seems to be the case because for each character of the string of length $n$, you ...

I need to prove that $L = \{ww^R\#ww^R \; | \; w \text{ is in } \{a,b\}^*\}$ is not context free.
I have tried using the pumping lemma for this.
For $w=a^pb^pb^pa^p\#a^pb^pb^pa^p$.
I have two cases ...